Geometry & Topology, Vol. 7 (2003)
Paper no. 19, pages 645--711.

Calculus III: Taylor Series

Thomas G Goodwillie

Abstract.
We study functors from spaces to spaces or spectra that preserve weak
homotopy equivalences. For each such functor we construct a universal
n-excisive approximation, which may be thought of as its n-excisive
part. Homogeneous functors, meaning n-excisive functors with trivial
(n-1)-excisive part, can be classified: they correspond to symmetric
functors of n variables that are reduced and 1-excisive in each
variable. We discuss some important examples, including the identity
functor and Waldhausen's algebraic K-theory.